Question

use transformations of ( f(x) = sqrt{x} ) to graph the following function. ( g(x) = sqrt{x} - 4 ) choose the correct graph below. a. b. c. d. (with four graphs labeled a, b, c, d)

Explanation:

Step1: Analyze the parent function

The parent function is \( f(x)=\sqrt{x} \), which has a domain \( x\geq0 \) and starts at the origin \((0,0)\), increasing slowly.

Step2: Analyze the transformation

The function \( g(x)=\sqrt{x}-4 \) is a vertical shift of the parent function \( f(x)=\sqrt{x} \) down by 4 units. So the vertex (starting point) of \( g(x) \) should be at \((0, - 4)\) instead of \((0,0)\) for \( f(x) \).

Step3: Analyze the graphs

• Graph A: Check the starting point. If it's shifted down, the y - intercept should be lower.
• Graph B: Doesn't seem to be a square - root function shape.
• Graph C: Let's check the starting point. The square - root function \( y = \sqrt{x}-4 \) starts at \( x = 0,y=-4 \) and increases. Looking at the grid, we can see the shape of the square - root function shifted down.
• Graph D: Doesn't have the correct square - root function shape.

Answer:

C (assuming C is the graph with the square - root shape starting at (0, - 4) and increasing)